Warming the stones at Brough Castle

 We visited Brough Castle on a warm day. The stones in the wall at the bottom of the wooden stair felt warm to the touch.I'm going to estimate warm as 30 degrees Celsius and say that it is therefore about 10 degrees above the air temperature.

The sandstone block is about 20cm long. Let's assume it is a cube of volume 8000 cubic centimetres. The density of sandstone is about 2.5 grams per cubic centimetre giving the block a mass of 20kg. Energy to heat it = mass x specific heat capacity x temperature rise = 20 x 920 x 10 = 184 000J. Assume the Sun was working at 1000 watts per square metre. The area of the block is 400 square cm so the block front gets 40W. It would take 184000/40 = 4600 seconds which is about 1.5 hours to heat the block. That's reasonable. It doesn't account for the conductivity of the block so perhaps the heated volume and thus mass is lower.